vendor/cranelift-codegen/src/opts/bitops.isle

;; Rewrites for `band`, `bnot`, `bor`, `bxor`

;; x | 0 == 0 | x == x | x == x.
(rule (simplify (bor ty
                     x
                     (iconst ty (u64_from_imm64 0))))
      (subsume x))
(rule (simplify (bor ty
                     (iconst ty (u64_from_imm64 0))
                     x))
      (subsume x))
(rule (simplify (bor ty x x))
      (subsume x))

;; x ^ 0 == 0 ^ x == x.
(rule (simplify (bxor ty
                     x
                     (iconst ty (u64_from_imm64 0))))
      (subsume x))
(rule (simplify (bxor ty
                     (iconst ty (u64_from_imm64 0))
                     x))
      (subsume x))

;; x ^ x == 0.
(rule (simplify (bxor (fits_in_64 (ty_int ty)) x x))
      (subsume (iconst ty (imm64 0))))

;; x ^ not(x) == not(x) ^ x == x | not(x) == not(x) | x == -1.
;; This identity also holds for non-integer types, vectors, and wider types.
;; But `iconst` is only valid for integers up to 64 bits wide.
(rule (simplify (bxor (fits_in_64 (ty_int ty)) x (bnot ty x))) (subsume (iconst ty (imm64 (ty_mask ty)))))
(rule (simplify (bxor (fits_in_64 (ty_int ty)) (bnot ty x) x)) (subsume (iconst ty (imm64 (ty_mask ty)))))
(rule (simplify (bor (fits_in_64 (ty_int ty)) x (bnot ty x))) (subsume (iconst ty (imm64 (ty_mask ty)))))
(rule (simplify (bor (fits_in_64 (ty_int ty)) (bnot ty x) x)) (subsume (iconst ty (imm64 (ty_mask ty)))))

;; x & -1 == -1 & x == x & x == x.
(rule (simplify (band ty x x)) (subsume x))
(rule (simplify (band ty x (iconst ty k)))
      (if-let -1 (i64_sextend_imm64 ty k))
      (subsume x))
(rule (simplify (band ty (iconst ty k) x))
      (if-let -1 (i64_sextend_imm64 ty k))
      (subsume x))

;; x & 0 == 0 & x == x & not(x) == not(x) & x == 0.
(rule (simplify (band ty _ zero @ (iconst ty (u64_from_imm64 0)))) (subsume zero))
(rule (simplify (band ty zero @ (iconst ty (u64_from_imm64 0)) _)) (subsume zero))
(rule (simplify (band (fits_in_64 (ty_int ty)) x (bnot ty x))) (subsume (iconst ty (imm64 0))))
(rule (simplify (band (fits_in_64 (ty_int ty)) (bnot ty x) x)) (subsume (iconst ty (imm64 0))))

;; not(not(x)) == x.
(rule (simplify (bnot ty (bnot ty x))) (subsume x))

;; DeMorgan's rule (two versions):
;; bnot(bor(x, y)) == band(bnot(x), bnot(y))
(rule (simplify (bnot ty (bor ty x y)))
      (band ty (bnot ty x) (bnot ty y)))
;; bnot(band(x, y)) == bor(bnot(x), bnot(y))
(rule (simplify (bnot ty (band t x y)))
      (bor ty (bnot ty x) (bnot ty y)))

;; `or(and(x, y), not(y)) == or(x, not(y))`
(rule (simplify (bor ty
                     (band ty x y)
                     z @ (bnot ty y)))
      (bor ty x z))
;; Duplicate the rule but swap the `bor` operands because `bor` is
;; commutative. We could, of course, add a `simplify` rule to do the commutative
;; swap for all `bor`s but this will bloat the e-graph with many e-nodes. It is
;; cheaper to have additional rules, rather than additional e-nodes, because we
;; amortize their cost via ISLE's smart codegen.
(rule (simplify (bor ty
                     z @ (bnot ty y)
                     (band ty x y)))
      (bor ty x z))

;; `or(and(x, y), not(y)) == or(x, not(y))` specialized for constants, since
;; otherwise we may not know that `z == not(y)` since we don't generally expand
;; constants in the e-graph.
;;
;; (No need to duplicate for commutative `bor` for this constant version because
;; we move constants to the right.)
(rule (simplify (bor ty
                     (band ty x (iconst ty (u64_from_imm64 y)))
                     z @ (iconst ty (u64_from_imm64 zk))))
      (if-let $true (u64_eq (u64_and (ty_mask ty) zk)
                            (u64_and (ty_mask ty) (u64_not y))))
      (bor ty x z))

;; (x ^ -1) can be replaced with the `bnot` instruction
(rule (simplify (bxor ty x (iconst ty k)))
  (if-let -1 (i64_sextend_imm64 ty k))
  (bnot ty x))

;; sshr((x | -x), N) == bmask(x) where N = ty_bits(ty) - 1.
;;
;; (x | -x) sets the sign bit to 1 if x is nonzero, and 0 if x is zero. sshr propagates
;; the sign bit to the rest of the value.
(rule (simplify (sshr ty (bor ty x (ineg ty x)) (iconst ty (u64_from_imm64 shift_amt))))
      (if-let $true (u64_eq shift_amt (u64_sub (ty_bits ty) 1)))
      (bmask ty x))

(rule (simplify (sshr ty (bor ty (ineg ty x) x) (iconst ty (u64_from_imm64 shift_amt))))
      (if-let $true (u64_eq shift_amt (u64_sub (ty_bits ty) 1)))
      (bmask ty x))

;; Matches any expressions that preserve "truthiness".
;; i.e. If the input is zero it remains zero, and if it is nonzero it can have
;; a different value as long as it is still nonzero.
(decl pure multi truthy (Value) Value)
(rule (truthy (sextend _ x)) x)
(rule (truthy (uextend _ x)) x)
(rule (truthy (bmask _ x)) x)
(rule (truthy (ineg _ x)) x)
(rule (truthy (bswap _ x)) x)
(rule (truthy (bitrev _ x)) x)
(rule (truthy (popcnt _ x)) x)
(rule (truthy (rotl _ x _)) x)
(rule (truthy (rotr _ x _)) x)
(rule (truthy (select _ x (iconst _ (u64_from_imm64 (u64_nonzero _))) (iconst _ (u64_from_imm64 0)))) x)
;; (ne ty (iconst 0) v) is also canonicalized into this form via another rule
(rule (truthy (ne _ x (iconst _ (u64_from_imm64 0)))) x)

;; All of these expressions don't care about their input as long as it is truthy.
;; so we can remove expressions that preserve that property from the input.
(rule (simplify (bmask ty v)) (if-let x (truthy v)) (bmask ty x))
(rule (simplify (select ty v t f)) (if-let c (truthy v)) (select ty c t f))
;; (ne ty (iconst 0) v) is also canonicalized into this form via another rule
(rule (simplify (ne cty v (iconst _ (u64_from_imm64 0))))
      (if-let c (truthy v))
      (if-let (value_type ty) c)
      (ne cty c (iconst ty (imm64 0))))



;; (sextend (bmask x)) can be replaced with (bmask x) since bmask
;; supports any size of output type, regardless of input.
;; Same with `ireduce`
(rule (simplify (sextend ty (bmask _ x))) (bmask ty x))
(rule (simplify (ireduce ty (bmask _ x))) (bmask ty x))

;; (bswap (bswap x)) == x
(rule (simplify (bswap ty (bswap ty x))) (subsume x))

;; (bitrev (bitrev x)) == x
(rule (simplify (bitrev ty (bitrev ty x))) (subsume x))